How can I derive the second degree equation for a curve if I know the slope at two points and the x and y-intercepts = 0?
2026-03-31 07:57:42.1774943862
How can I derive the second degree equation for a curve if I know the slope at two points and the y-intercept = 0?
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Say that the equation is $$f(x)=ax^2+bx+c$$ which makes $$f'(x)=2ax+b$$ So, now consider three points $( x_1,x_2,x_3)$. You then have $$f'(x_1)=2ax_1+b$$ $$f'(x_2)=2ax_2+b$$ $$f(x_3)=ax_3^2+bx_3+c$$ and you know the value of each lhs.
I am sure that you can take it from here.